Mathematical models for the membranes of invertebrate nerve cells displaying the periodic activity pattern known as "bursting" will be investigated. These models will be based on a similar model developed by the principal investigator in collaboration with M. Kim for a bursting neuron in the mollusc Aplysia. Two parallel lines of inquiry will be followed. The first will consist of a refinement of the original model to account for recently published experimental observations. The second will be an attempt to apply the concepts of the model to the problem of simulating interconnected systems of nerve cells which display bursting, although the individual cells in isolation do not.